CN115795399B - A method and system for adaptive fusion of multi-source remote sensing precipitation data - Google Patents

Abstract

The present application relates to the technical field of identification methods or devices using electronic equipment, and provides a multi-source remote sensing precipitation data adaptive fusion method and system. Based on the error characteristics of multi-source remote sensing precipitation data, the method adaptively adjusts the corresponding weight of each precipitation data, and calculates the adaptive feature fusion data of multi-source remote sensing precipitation data based on the weight, and then combines the precipitation influencing factors to perform adaptive feature fusion The final precipitation data is optimized and downscaled, and the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data is obtained. Finally, the downscaling result is used as the initial condition of the HASM method after parameter optimization, and the observation value of the meteorological station is used As an optimal control condition, a multi-source precipitation fusion model is constructed. This fusion model breaks through the limitations of the traditional precipitation data fusion model that needs to be established on certain assumptions, and can obtain the optimal estimation of the spatial distribution of precipitation with high temporal and spatial resolution and low uncertainty.

Description

A method and system for adaptive fusion of multi-source remote sensing precipitation data

Technical Field

The present application relates to the technical field of methods or devices for identifying using electronic devices, and in particular to a method and system for adaptively fusing multi-source remote sensing precipitation data.

Background Art

Precipitation is an important component of energy exchange and water cycle in the climate system, an important indicator of climate change, and has a very important impact on human activities and socioeconomic development. High-quality information on the temporal and spatial distribution of precipitation is of great significance for the study of climate, meteorology, ecology, and hydrology. At the same time, as an indispensable basic data in the cross-disciplinary integration of atmospheric science, hydrology, geology, and ecology, precipitation data on fine temporal and spatial scales are important driving parameters for various research models, and the estimation accuracy of precipitation data has a very important impact on the simulation results of research models. my country has a vast territory, is located in the East Asian monsoon region, and spans multiple climate zones. Affected by multiple factors such as sea and land location, topography, monsoon, underlying surface, and human activities, precipitation presents complex temporal and spatial variation characteristics, especially the daily precipitation process presents obvious randomness and temporal and spatial differences. Accurately obtaining information on the temporal and spatial characteristics of precipitation is an important basis for hydrological and water resources management, flood and drought detection, geological disaster warning, and risk assessment.

With the rapid development of meteorological observation systems, more and more data are obtained using ground meteorological stations, radars and satellites. In addition, with the continuous advancement of technical methods, a large amount of multi-source and multi-scale precipitation data has been accumulated. These precipitation data have different temporal and spatial resolutions, and show different accuracy characteristics for precipitation in the same region. At present, integrating precipitation observation information or estimation information from different sources, different accuracies, and different temporal and spatial resolutions through certain optimization criteria to obtain high-precision spatial distribution data of precipitation at fine temporal and spatial scales is a frontier issue and scientific difficulty in the field of global change research, and has great development potential.

Since the 1990s, the concept of multi-source precipitation data fusion has been introduced into the quantitative estimation of precipitation space, providing an important idea for estimating the spatial distribution of precipitation based on multi-source information. Data fusion has become an important means of obtaining the same target information from multi-source data due to its advantages of wide temporal and spatial coverage, high credibility, reducing uncertainty in data information, and improving temporal and spatial resolution of data. Under the framework of precipitation fusion, precipitation data from different sources such as ground observations or remote sensing measurements are integrated into the quantitative model, and a more reasonable estimate of the true distribution of precipitation is obtained through complementary advantages and reasonable matching.

At present, scholars at home and abroad have successively carried out a series of studies on the fusion of satellite and ground multi-source precipitation data. Common fusion methods include objective analysis method, probability density method, optimal weight method, conditional fusion method, geostatistical method, Bayesian estimation method and machine learning-based methods. These fusion methods all combine certain premise assumptions with specific fusion methods to obtain the optimal estimate of the true distribution of precipitation. However, the above fusion methods do not take into account the spatiotemporal variation characteristics of precipitation data, nor do they fully consider the different accuracy characteristics of precipitation data in the same region, resulting in the accuracy of the fusion model still has room for improvement.

Therefore, it is necessary to provide a technical solution that can fully utilize the advantages of more different data sources to obtain precipitation spatial distribution information with high temporal and spatial resolution and low uncertainty.

Summary of the invention

The purpose of this application is to provide a method and system for adaptive fusion of multi-source remote sensing precipitation data. The system fully considers the different accuracy characteristics of precipitation data in the same area, can give full play to the advantages of multiple different data sources, and obtains high-precision precipitation spatial distribution data at fine spatiotemporal scales from precipitation observation information or estimation information with different sources, different accuracy, and different spatiotemporal resolutions.

In order to achieve the above objectives, this application provides the following technical solutions:

The present application provides a method for adaptively fusing multi-source remote sensing precipitation data, including:

Based on the error characteristics of multi-source remote sensing precipitation data, the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data is calculated using the Lagrange multiplier method;

Based on the multi-source remote sensing precipitation data and the weights corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data, the adaptive feature fusion data of the multi-source remote sensing precipitation data is calculated;

Using the geographically weighted ridge regression method, the adaptive feature fusion data of the multi-source remote sensing precipitation data is downscaled in combination with the influencing factors of precipitation, so as to obtain the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data;

According to the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with the improved high-precision surface modeling method, a multi-source precipitation fusion model is constructed.

Preferably, the geographically weighted ridge regression method is used to downscale the adaptive feature fusion data of the multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, so as to obtain the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data, specifically:

，

,

Downscaling the adaptive feature fusion data of the multi-source remote sensing precipitation data;

为地理加权岭回归方法构建的回归函数；v为所述多源遥感降水数据的自适应特征融合数据；covariate为协变量集合，即降水的影响因素构成的集合；x ₀ 为所述多源遥感降水数据的自适应特征融合数据的降尺度结果。In the formula,

is the regression function constructed by the geographically weighted ridge regression method; v is the adaptive feature fusion data of the multi-source remote sensing precipitation data; covariate is the covariate set, that is, the set of factors affecting precipitation; x0 is the _downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data.

Preferably, the expression of the multi-source precipitation fusion model is as follows:

，

,

为地理加权岭回归方法构建的回归函数；v为所述多源遥感降水数据的自适应特征融合数据；covariate为协变量集合，即降水的影响因素构成的集合；x ⁰ 为所述多源遥感降水数据的自适应特征融合数据的降尺度结果，作为高精度曲面建模方法当前迭代对应的降水空间分布初始曲面；H、L分别为高精度曲面建模方法对应的模拟曲面上各网格点上、下界。Wherein: A, B, C are coefficients of the finite difference equations corresponding to the high-precision surface modeling method; d, q, p are the right-hand side terms of the finite difference equations corresponding to the high-precision surface modeling method; x ⁿ⁺¹ represents the value of the n+1th iteration of each grid point on the simulation surface corresponding to the high-precision surface modeling method; S is the sampling matrix; g is the sampling vector;

is the regression function constructed by the geographically weighted ridge regression method; v is the adaptive feature fusion data of the multi-source remote sensing precipitation data; covariate is a set of covariates, that is, a set of factors affecting precipitation ^; x0 is the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data, which serves as the initial surface of the precipitation spatial distribution corresponding to the current iteration of the high-precision surface modeling method; H and L are respectively the upper and lower bounds of each grid point on the simulation surface corresponding to the high-precision surface modeling method.

Preferably, the error characteristic of the multi-source remote sensing precipitation data is expressed as follows:

，

,

Wherein: σ ² is the mean square error; E represents the expected value; u represents the real precipitation data, ui represents the precipitation data from the i - th data source; _ωi represents the weight corresponding to the precipitation data from the i- th data source; v _represents the adaptive feature fusion data of the multi-source remote sensing precipitation data; k represents the total number of data sources.

Preferably, based on the error characteristics of multi-source remote sensing precipitation data, the Lagrange multiplier method is used to calculate the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data, specifically:

The Lagrange multiplier method is used to solve the expression of the error characteristics of the multi-source remote sensing precipitation data to obtain the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data. The expression of the weight is as follows:

，

,

分别为第i数据来源、第j数据来源的降水数据的均方差；ω _i 表示第i数据来源的降水数据对应的权重；k表示数据来源的总数。Where:

are the mean square errors of the precipitation data from the ith data source and the jth data source respectively; ω _i represents the weight corresponding to the precipitation data from the ith data source; k represents the total number of data sources.

Preferably, the expression of the adaptive feature fusion data of the multi-source remote sensing precipitation data is as follows:

，

,

分别为第i数据来源、第j数据来源的降水数据的均方差；u _i 表示第i数据来源的降水数据；k表示数据来源的总数。Wherein: v represents the adaptive feature fusion data of the multi-source remote sensing precipitation data;

are the mean square errors of the precipitation data from the ith data source and the jth data source respectively; ui represents the precipitation data from the ith data source; _k represents the total number of data sources.

Preferably, after constructing a multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with an improved high-precision surface modeling method, the method further includes:

The multi-source precipitation fusion model is solved by using a pre-conditioned conjugate gradient method and multiple iteration steps. Under the optimization control constraint of the meteorological station observation data, the initial surface x ⁰ of the precipitation spatial distribution is continuously adjusted to finally obtain the optimal estimation value of the precipitation spatial distribution.

Preferably, the process further comprises: for each iteration, performing the following processing on each grid point on the simulation surface:

If there is no meteorological station in the current grid point, the upper and lower bounds H and L of the current grid point are determined according to the relaxation coefficient of the high-precision surface modeling method and the extreme value of the neighboring grid points within the search radius of the high-precision surface modeling method;

Wherein, the search radius is the number of adjacent grid points that need to be searched when the high-precision surface modeling method determines the upper and lower bounds H and L of the current grid point;

。If the number of meteorological stations in the current grid point is less than the preset threshold, the value of the neighboring grid point within the search radius is defined as the average of the observation value of the existing meteorological station within the radius and the grid point value of the multi-source remote sensing precipitation data within the search radius, and x ⁿ⁺¹ satisfies the inequality

.

Preferably, for each iteration, the sampling point weights corresponding to each meteorological station are determined by the following steps:

Calculate the average value of the neighboring grid points of each meteorological station on the current iteration simulation surface;

The difference between the observed data of each meteorological station and the average value is calculated, and the calculated difference is used as the sampling point weight corresponding to each meteorological station.

The embodiment of the present application also provides a multi-source remote sensing precipitation data adaptive fusion system, including:

A weight calculation unit is configured to calculate the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data by using the Lagrange multiplier method based on the error characteristics of the multi-source remote sensing precipitation data;

An adaptive feature fusion unit is configured to calculate adaptive feature fusion data of the multi-source remote sensing precipitation data based on the multi-source remote sensing precipitation data and the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data;

The data optimization unit is configured to use a geographically weighted ridge regression method to downscale the adaptive feature fusion data of the multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, so as to obtain a downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data;

The model building unit is configured to build a multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data in combination with an improved high-precision surface modeling method.

Beneficial effects:

In the above technical scheme in the present application, based on the error characteristics of multi-source remote sensing precipitation data, the Lagrange multiplier method is used to calculate the weight corresponding to the precipitation data; and based on the weight and the multi-source remote sensing precipitation data, the adaptive feature fusion data is calculated; then the geographically weighted ridge regression method is used to downscale the adaptive feature fusion data of the multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, and the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data are obtained; according to the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with the improved high-precision surface modeling method, a multi-source precipitation fusion model is constructed. This method can adaptively adjust the weights corresponding to each data source according to the error characteristics of the precipitation data from multiple sources, and make full use of the high-precision simulation advantages of the high-precision surface modeling method to construct a multi-source precipitation fusion model that can fuse high-dimensional precipitation data. This model breaks through the limitation that the existing precipitation data fusion model needs to be established on certain premise assumptions, and at the same time breaks through the limitation that the current precipitation data fusion model is limited to two or three sources. It can effectively fuse precipitation data from multiple sources (three or more) and multiple scales, thus providing a high-precision fusion method for high-dimensional, multi-source and multi-scale precipitation data.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings constituting part of the present application are used to provide a further understanding of the present application. The exemplary embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. Among them:

FIG1 is a schematic diagram of a flow chart of a method for adaptively fusing multi-source remote sensing precipitation data according to some embodiments of the present application;

FIG2 is a logic diagram of a method for adaptively fusing multi-source remote sensing precipitation data according to some embodiments of the present application;

FIG3 is a schematic diagram of the structure of a multi-source remote sensing precipitation data adaptive fusion system provided according to some embodiments of the present application.

DETAILED DESCRIPTION

The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. Each example is provided by way of explanation of the present application but does not limit the present application. In fact, it will be clear to those skilled in the art that modifications and variations may be made in the present application without departing from the scope or spirit of the present application. For example, a feature shown or described as a part of an embodiment may be used in another embodiment to produce yet another embodiment. Therefore, it is desired that the present application includes such modifications and variations within the scope of the appended claims and their equivalents.

As described in the background technology, the common fusion methods for satellite and ground multi-source precipitation data are: objective analysis method, probability density method, optimal weight method, conditional fusion method, geostatistical method, Bayesian estimation method and machine learning-based method, etc. The assumptions and specific fusion methods of these fusion methods are different, but the basic ideas are the same: most of them are based on certain premise assumptions, by constructing a background field of precipitation data, using optimization schemes combined with ground measured data to correct the background field, and then obtaining the optimal estimate of the true distribution of precipitation. Since these fusion methods are all based on certain premise assumptions, they bring certain uncertainties to the model.

In addition, most of the current research on the fusion of multi-source precipitation data is based on the fusion of two or three data products from station and remote sensing data or model results using different methods. There are few studies on the high-precision fusion of data products from more than three sources, which also leads to the current massive multi-source and multi-scale precipitation estimation products not being fully and effectively utilized. In addition, most of the current fusion models do not consider the error characteristics of precipitation data from different sources, so as to more accurately and effectively utilize different data characteristics for high-precision fusion.

With the rapid development of meteorological observation systems, more and more precipitation data are obtained using ground meteorological stations, radars, satellites, etc., and the quality of data simulated by various numerical models is also constantly improving. In the case of rapid growth in the scale of precipitation data, combining multidisciplinary research ideas, giving full play to the advantages of more different data sources, and studying effective fusion methods for multi-source and multi-scale precipitation data to obtain precipitation spatial distribution information with high temporal and spatial resolution and small uncertainty will help enrich and develop the current theoretical and methodological framework of precipitation simulation, and can provide effective data support for the smooth implementation of regional disaster prevention and mitigation, the rational development and utilization of water resources, and climate change assessment. It can also provide a methodological reference for the fusion research of other geographic environmental variables.

To this end, the present application provides a method and system for adaptive fusion of multi-source remote sensing precipitation data. The method can perform high-precision fusion of high-dimensional data based on the error characteristics of the multi-source remote sensing precipitation data itself, and can be used in the fields of spatial distribution simulation of climate elements, ecological environment elements, and geographical terrain elements under the background of big data. It can also be regarded as a method of surface grid approximation, and is used for large-scale multi-source surface approximation modeling in physics, chemistry, medicine, etc.

Exemplary Methods

The present application embodiment provides a method for adaptively fusing multi-source remote sensing precipitation data, as shown in FIG1 and FIG2 , the method comprising:

Step S101: Based on the error characteristics of multi-source remote sensing precipitation data, the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data is calculated using the Lagrange multiplier method.

It should be noted that multi-source remote sensing precipitation data can also be called multi-source, multi-scale precipitation data. Among them, multi-scale precipitation data can be precipitation data with different spatial resolutions or different temporal resolutions. In the precipitation data fusion process, precipitation data from different sources are expressed in multiple data dimensions. High dimensions can be understood as precipitation data coming from multiple sources. Further, high dimensions can be understood as more than three data sources, and precipitation data from different sources also have different data structures.

In the embodiments of the present application, the error characteristics of multi-source remote sensing precipitation data can be expressed in a variety of error ways, such as mean square error, root mean square error, mean square deviation, etc.

Specifically, when the mean square error is used to express the error characteristics of multi-source remote sensing precipitation data, it is assumed that the multi-source remote sensing precipitation data obtained is u _i , i=1,2,…k , k is the number of precipitation data sources, the mean and variance of each precipitation data are e _i , σ _i respectively, and the data obtained after the adaptive feature fusion of multi-source remote sensing precipitation data is v , then the mean square error after fusion can be expressed as:

（1）

(1)

；v表示多源遥感降水数据的自适应特征融合数据；k表示数据来源的总数。Where: σ ² is the mean square error; E is the expected value; u is the real precipitation data, ui is the precipitation data from the ith data source _; ωi _is the weight corresponding to the precipitation data from the ith data source, and

; v represents the adaptive feature fusion data of multi-source remote sensing precipitation data; k represents the total number of data sources.

Taking the weights in formula (1) as common factors, we get:

（2）

(2)

To obtain a weight expression, in an embodiment of the present application, the Lagrange multiplier method is used to solve the expression of the error characteristics of multi-source remote sensing precipitation data to obtain the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data.

Specifically, using the Lagrange multiplier method, formula (2) is converted into the following function form:

（3）

(3)

Where λ is the Lagrange multiplier.

By taking the derivatives of ωi _and λ in the function of formula (3) and setting them to 0, we can obtain the following set of equations:

（4）

(4)

（5）

(5)

Then, by solving formula (4) and formula (5), the expression of weight is obtained as follows:

（6）

(6)

分别为第i数据来源、第j数据来源的降水数据的均方差；ω _i 表示第i数据来源的降水数据对应的权重；k表示数据来源的总数。Where:

are the mean square errors of the precipitation data from the ith data source and the jth data source respectively; ω _i represents the weight corresponding to the precipitation data from the ith data source; k represents the total number of data sources.

Step S102: Based on the multi-source remote sensing precipitation data and the weights corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data, adaptive feature fusion data of the multi-source remote sensing precipitation data is calculated.

Specifically, based on the weight expression of formula (6), the expression of adaptive feature fusion data of multi-source remote sensing precipitation data is obtained as follows:

（7）

(7)

分别为第i数据来源、第j数据来源的降水数据的均方差；u _i 表示第i数据来源的降水数据；k表示数据来源的总数。Where: v represents the adaptive feature fusion data of multi-source remote sensing precipitation data;

are the mean square errors of the precipitation data from the ith data source and the jth data source respectively; ui represents the precipitation data from the ith data source; _k represents the total number of data sources.

In this embodiment, the error characteristics of precipitation data from various sources are first expressed, and then the weights of precipitation data from various data sources are adaptively calculated based on the error characteristics of the fused data sources, laying the foundation for the subsequent construction of a high-precision multi-source precipitation fusion model.

Step S103: using the geographically weighted ridge regression method, the adaptive feature fusion data of multi-source remote sensing precipitation data is downscaled in combination with the influencing factors of precipitation, so as to obtain the downscaling result of the adaptive feature fusion data of multi-source remote sensing precipitation data.

Geographically weighted ridge regression (GWRR) shrinks the impact of redundant explanatory variables by limiting the range of regression parameters. It is a technique that uses ridge parameters to locally compensate for geographically weighted regression (GWR) models to improve the accuracy of GWR models and solve the multicollinearity problem of regression coefficients in GWR models.

In the embodiment of the present application, the geographically weighted ridge regression method is used to downscale the adaptive feature fusion data of multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, and the downscaling result of the adaptive feature fusion data of multi-source remote sensing precipitation data is obtained, which is specifically:

According to the following expression:

（8）

(8)

Downscaling of adaptive feature fusion data of multi-source remote sensing precipitation data;

为地理加权岭回归方法构建的回归函数；v为多源遥感降水数据的自适应特征融合数据；covariate为协变量集合，即降水的影响因素构成的集合；x ₀ 为多源遥感降水数据的自适应特征融合数据的降尺度结果。In the formula,

is the regression function constructed by the geographically weighted ridge regression method; v is the adaptive feature fusion data of multi-source remote sensing precipitation data; covariate is the covariate set, that is, the set of factors affecting precipitation _; x0 is the downscaling result of the adaptive feature fusion data of multi-source remote sensing precipitation data.

Among them, the influencing factors of precipitation may include cloud amount, cloud optical thickness, effective radius of cloud particles, cloud top temperature, cloud top pressure, cloud water path, 500hPa and 800hPa potential heights, air temperature, latent heat flux, sensible heat flux, shortwave radiation, longwave radiation, relative humidity, maximum relative humidity, minimum relative humidity, specific humidity (ground, 500hPa and 800hPa), sea level pressure, wind speed, elevation, slope, longitude, latitude, distance to the coastline, Normalized Difference Vegetation Index (NDVI), etc.

Step S104: construct a multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data in combination with the improved high-precision surface modeling method.

Among them, the meteorological station observation data is collected through ground meteorological stations. The meteorological stations are equipped with a variety of sensors for meteorological observation, which can observe the meteorological element values of the atmosphere close to the ground and some phenomena in the free atmosphere, and can collect meteorological data such as temperature, air pressure, air humidity, wind direction and speed, clouds, visibility, weather phenomena, precipitation, evaporation, sunshine, snow depth, ground temperature, etc.

It should be noted that the High Accuracy Surface Modelling (HASM) method is a surface modeling method based on the principles of differential geometry and optimization control theory. It uses global approximate data (including remote sensing data and coarse-resolution simulation data of global models) as the driving field and local high-precision data (including monitoring network data and survey sampling data) as the optimization control conditions. This method solves the error and multi-scale problems that have plagued surface modeling for half a century, and has refined and formed the basic theorem of earth surface modeling based on a large number of applications over the past 20 years.

Specifically, according to the basic theorem of surface theory, assuming that the first basic quantities E, F, G and the second basic quantities L, M , N of the surface satisfy symmetry, E, F, G are positive definite, E, F, G, L, M and N satisfy the Gauss equations, then the total differential equations under the initial conditions of f (x, y) = f (x ₀ , y ₀ ) , ( x = x ₀ , y = y ₀ ), there is a unique solution z = f (x, y) .

The expression of Gauss equations is:

（9）

(9)

，in:

,

，

,

为第二类克里斯托弗尔符号。Where: f _x , f _y are the first-order partial derivatives of f in the x and y directions, f _xx , f _yy are the second-order partial derivatives of f in the x and y directions, f _xy is the mixed partial derivative of f in the x and y directions,

It is a Christopher symbol of the second kind.

是计算域

的正交剖分、

为无量纲标准化的计算域、

为计算步长、

为标准化计算域的栅格（也叫网格点），则第一类基本量的有限差分逼近为：like

Is the computational domain

Orthogonal decomposition of

is the dimensionless normalized computational domain,

To calculate the step length,

is the grid (also called grid point) of the standardized computational domain, then the finite difference approximation of the first kind of basic quantity is:

，

,

The finite difference approximation of the second type of basic quantity is:

，

,

The finite difference of the second kind of Christophel symbol can be expressed as:

The finite difference form of the Gauss equations is:

（10）

(10)

The matrix form of the above formula (10) can be written as:

（11）

(11)

，in:

,

，

,

，

,

Combined with the effective constraint control of local high-precision data (such as monitoring network data and survey sampling data), the constrained least squares problem of the above formula (11) can be expressed as the least squares problem of equality constraints solved by HASM, as shown in formula (12):

（12）

(12)

是

在第m采样点（x _i ，y _j ）的值，则S _{m，（i-1）×J+j} =1，

。Where S is the sampling matrix, g is the sampling vector, A, B, C are the coefficients of the HASM finite difference equations; d, q, p are the right-hand side terms of the HASM finite difference equations. If

yes

The value at the mth sampling point ( xi _, yj ₎ , then Sm _{, (i-1) × J + j} = 1,

.

Therefore, HASM is finally converted into an equality-constrained least squares problem constrained by ground sampling, in order to keep the overall simulation error to a minimum while ensuring that the simulation value at the sampling point is equal to the sampling value. This method makes full use of sampling information and is an effective means to ensure that the iteration approaches the optimal simulation effect.

Using the method of normal equations, the constrained least squares problem expressed by formula (12) can be transformed into:

（13）

(13)

，θ为气象站点的权重系数。in,

, θ is the weight coefficient of the meteorological station.

After the downscaling results of the adaptive feature fusion data of multi-source remote sensing precipitation data are obtained in the above steps, the HASM method based on formula (12) takes the downscaling results of the adaptive feature fusion data of multi-source remote sensing precipitation data as the initial conditions of HASM, and the meteorological station observation data (i.e., sampling data) as the optimization control conditions. At the same time, a high-order finite difference format is used for discretization at the boundary of the simulation area, and the upper and lower bounds of each grid point on the simulation surface are controlled according to the downscaling results of the adaptive feature fusion data of multi-source remote sensing precipitation data. The expression of the multi-source precipitation fusion model is obtained as follows:

（14）

(14)

为地理加权岭回归方法构建的回归函数；v为多源遥感降水数据的自适应特征融合数据；covariate为协变量集合，即降水的影响因素构成的集合；x ⁰ 为多源遥感降水数据的自适应特征融合数据的降尺度结果，作为高精度曲面建模方法当前迭代对应的降水空间分布初始曲面；H、L分别为高精度曲面建模方法对应的模拟曲面上各网格点上、下界，由等高线控制得到。Wherein: A, B, C are coefficients of the finite difference equations corresponding to the high-precision surface modeling method; d, q, p are the right-hand side terms of the finite difference equations corresponding to the high-precision surface modeling method; x ⁿ⁺¹ represents the value of the n+1th iteration of each grid point on the simulation surface corresponding to the high-precision surface modeling method; S is the sampling matrix; g is the sampling vector;

is the regression function constructed by the geographically weighted ridge regression method; v is the adaptive feature fusion data of multi-source remote sensing precipitation data; covariate is the covariate set, that is, the set of factors affecting precipitation ^; x0 is the downscaling result of the adaptive feature fusion data of multi-source remote sensing precipitation data, which serves as the initial surface of precipitation spatial distribution corresponding to the current iteration of the high-precision surface modeling method; H and L are the upper and lower bounds of each grid point on the simulation surface corresponding to the high-precision surface modeling method, respectively, which are controlled by the contour lines.

It should be noted that traditional HASM is mostly used for station data interpolation research. It uses the effective information of the station to construct the simulated surface through the surface equation, which is essentially an interpolation method. In the embodiment of the present application, the high-precision simulation advantage of HASM is fully utilized and combined with the adaptive feature fusion data of multi-source remote sensing precipitation data to obtain a fusion model that can be used to effectively fuse high-dimensional, multi-source, and multi-scale precipitation data, thereby giving full play to the advantages of multiple different data sources to obtain precipitation spatial distribution information with high spatiotemporal resolution and low uncertainty.

To solve the multi-source precipitation fusion model, in some embodiments, after constructing the multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with the improved high-precision surface modeling method, the method further includes: solving the multi-source precipitation fusion model using a pre-processed conjugate gradient method and multiple iteration steps, and continuously adjusting the initial surface x ⁰ of the precipitation spatial distribution under the optimization control constraint of the meteorological station observation data, and finally obtaining the optimal estimate value X ^(*) of the precipitation spatial distribution.

It should be noted that, in the past, HASM was used as an interpolation method. In the first iteration, the right-hand terms d, q, and p in the basic equation group (i.e., the equation group represented by formula (12)) were initialized to 0, that is, the initial value of the iteration in the numerical simulation solution was zero. In the multi-source precipitation fusion model constructed in this application, i.e., formula (14), the specific value of the iteration of the initial condition X ⁽⁰⁾ is calculated by the initial surface x ⁰ of the spatial distribution of precipitation, and the initial surface x ⁰ of the spatial distribution of precipitation is obtained by geographically weighting the downscaling results of the adaptive feature fusion data of multi-source remote sensing precipitation data, and then fusing them with the geographical topography and other influencing factors of precipitation. Therefore, using X ⁽⁰⁾ as the initial value of the iteration of HASM to solve the model can greatly improve the accuracy of the fusion result.

。The search radius and the upper and lower bounds of each grid point are important hyperparameters of the HASM method. In the past, when HASM was iteratively solved, the search radius was usually set to a fixed value, and the default setting was 12. In the embodiment of the present application, the value of the search radius can be determined according to the heterogeneity of the regional precipitation distribution, and in the process of iterative solution, the upper and lower bounds of each grid point are determined in the following way: For each iteration, each grid point on the simulation surface is processed as follows: If there is no meteorological station in the current grid point, the upper and lower bounds H and L of the current grid point are determined according to the relaxation coefficient of the high-precision surface modeling method and the extreme values of the neighboring grid points within the search radius of the high-precision surface modeling method; wherein, the search radius is the number of neighboring grid points that need to be searched when the high-precision surface modeling method determines the upper and lower bounds H and L of the current grid point; if the number of meteorological stations in the current grid point is less than the preset threshold, the value on the neighboring point within the search radius is defined as the average of the observation value of the existing meteorological station within the radius and the grid point value of the multi-source remote sensing precipitation data within the search radius, and at the same time x ⁿ⁺¹ satisfies the inequality

.

。由此，根据多源遥感降水数据对各个网格点的上、下界进行约束，进一步提高融合模型求解的精度。Specifically, in the embodiment of the present application, considering that the number of meteorological stations is often limited, a relaxation coefficient with a value range of 0 to 1 is introduced. In the iterative solution process, for grid points on the simulated surface without meteorological stations, such as the grid points in high altitudes, uninhabited areas, complex terrain and other areas, the upper and lower bounds of the grid point value are determined according to the extreme value relaxation of the neighboring grid points within the search radius; for grid points where the number of meteorological stations is less than a preset threshold, that is, areas with sparse stations, the values on the neighboring grid points within the search radius are defined as the average of the existing meteorological station observations within the search radius and the grid point values of the multi-source remote sensing precipitation data within the search radius, and the inequality is satisfied at the same time:

Therefore, the upper and lower bounds of each grid point are constrained according to multi-source remote sensing precipitation data to further improve the accuracy of the fusion model solution.

In some embodiments, for each iteration, the sampling point weights corresponding to each meteorological station are determined by the following steps: calculating the average value of the neighboring grid point values of the locations of each meteorological station on the current iteration simulation surface; calculating the difference between the observed data of each meteorological station and the average value, and using the calculated difference as the sampling point weights corresponding to each meteorological station.

It should be noted that the sampling point weight is one of the hyperparameters of the HASM method. In the traditional HASM method solution process, the weight of each sampling point is usually set manually based on prior knowledge, and is generally set to a fixed integer value in the range of 1 to 10, with a default value of 2. In the embodiment of the present application, the sampling point is each meteorological station. In order to eliminate the influence of abnormal values in the observation data of each meteorological station, the difference between the observation data of each meteorological station and the average value of the neighboring grid point value of the corresponding meteorological station on the current iterative simulation surface is taken as the sampling point weight θ corresponding to the meteorological station, thereby further improving the accuracy of the fusion model.

On the basis of the aforementioned construction of the multi-source precipitation fusion model and parameter optimization, and under the optimization control constraints of the precipitation observations obtained at the meteorological stations, the fusion results based on the error characteristics of the multi-source remote sensing precipitation data and the background knowledge (geographically weighted in combination with the precipitation influencing factors) are used as the initial surface of the multi-source precipitation fusion model to drive the numerical simulator of the multi-source precipitation fusion model to iteratively solve. The solution process integrates the high-precision meteorological station observation data and the results of the adaptive feature fusion data correction of the multi-source remote sensing precipitation data using the GWRR method combined with background knowledge, thereby obtaining the fusion result of the multi-source precipitation data, that is, the optimal estimate of the spatial distribution of precipitation.

Exemplarily, referring to FIG2, the method provided by the present application may include the following steps: after obtaining remote sensing precipitation data from multiple (e.g., K ) sources, firstly, calculating the error and variance of the multi-source precipitation data to obtain the error characteristics of each precipitation data, then solving the weight coefficient of the precipitation data from each source using the Lagrange multiplier method according to the error characteristics, and performing adaptive feature fusion calculation based on the obtained weight coefficient to obtain the adaptive feature fusion data of the multi-source remote sensing precipitation data. Subsequently, the geographically weighted ridge regression method is used to integrate the precipitation influencing factors as background knowledge into the adaptive feature fusion data of the multi-source remote sensing precipitation data obtained in the above steps, and further optimize and downscale it to obtain the downscaled result of the adaptive feature fusion data of the multi-source remote sensing precipitation data; at the same time, the HASM method is optimized and improved by searching the radius, setting the upper and lower bounds, calculating the weight of the sampling point observation value, and using the meteorological station observation value as the optimization control condition. Finally, the downscaled result of the adaptive feature fusion data of the multi-source remote sensing precipitation data is used as the initial condition, combined with the improved HASM, to construct a multi-source precipitation fusion model. Through the above steps, the precipitation data obtained from high-precision meteorological station observations are used to further optimize the high-resolution precipitation spatial distribution surface data. The simulation results not only have the accuracy of the meteorological station data, but also take into account the regional precipitation distribution outside the meteorological station, realize the effective fusion of multi-source precipitation data, and enhance the characterization of precipitation in the study area.

In summary, in this application, based on the error characteristics of multi-source remote sensing precipitation data, the Lagrange multiplier method is used to calculate the weight corresponding to the precipitation data; and based on the weight and the multi-source remote sensing precipitation data, the adaptive feature fusion data is calculated; then the geographically weighted ridge regression method is used to downscale the adaptive feature fusion data of the multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, and the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data are obtained; according to the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with the high-improved precision surface modeling method, a multi-source precipitation fusion model is constructed. This method can adaptively adjust the weights corresponding to each data source according to the error characteristics of the precipitation data from multiple sources, and make full use of the high-precision simulation advantages of the high-precision surface modeling method to construct a multi-source precipitation fusion model that can fuse high-dimensional precipitation data. This model breaks through the limitation that the existing precipitation data fusion model needs to be established on certain premise assumptions, and at the same time breaks through the limitation that the current precipitation data fusion model is limited to two or three sources. It can effectively fuse precipitation data from multiple sources (three or more) and multiple scales, thus providing a new and high-precision fusion method for high-dimensional, multi-source and multi-scale precipitation data.

Exemplary Systems

The present application embodiment provides a multi-source remote sensing precipitation data adaptive fusion system, as shown in Figure 3, the system includes: a weight calculation unit 301, an adaptive feature fusion unit 302, a data optimization unit 303 and a model construction unit 304. Among them:

The weight calculation unit 301 is configured to calculate the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data by using the Lagrange multiplier method based on the error characteristics of the multi-source remote sensing precipitation data.

The adaptive feature fusion unit 302 is configured to calculate the adaptive feature fusion data of the multi-source remote sensing precipitation data based on the multi-source remote sensing precipitation data and the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data.

The data optimization unit 303 is configured to use the geographically weighted ridge regression method to downscale the adaptive feature fusion data of the multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, and obtain the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data.

The model building unit 304 is configured to build a multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data in combination with the improved high-precision surface modeling method.

The multi-source remote sensing precipitation data adaptive fusion system provided in the embodiment of the present application can implement the steps and processes of the multi-source remote sensing precipitation data adaptive fusion method provided in any of the above embodiments, and achieve the same technical effects, which will not be described one by one here.

The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (8)

1. A method for adaptively fusing multi-source remote sensing precipitation data, comprising: Based on the error characteristics of multi-source remote sensing precipitation data, the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data is calculated using the Lagrange multiplier method; The expression of the error characteristic of the multi-source remote sensing precipitation data is as follows:

, Where: σ ² is the mean square error; E represents the expected value; u represents the real precipitation data, u _i represents the precipitation data of the i - th data source; ω _i represents the weight corresponding to the precipitation data of the i- th data source; v represents the adaptive feature fusion data of the multi-source remote sensing precipitation data; k represents the total number of data sources; Based on the error characteristics of multi-source remote sensing precipitation data, the Lagrange multiplier method is used to calculate the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data, specifically: The Lagrange multiplier method is used to solve the expression of the error characteristics of the multi-source remote sensing precipitation data to obtain the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data. The expression of the weight is as follows:

,

, Where:

,

are the mean square error of the precipitation data from the ith data source and the jth data source respectively; ω _i represents the weight corresponding to the precipitation data from the ith data source; k represents the total number of data sources; Based on the multi-source remote sensing precipitation data and the weights corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data, the adaptive feature fusion data of the multi-source remote sensing precipitation data is calculated; Using the geographically weighted ridge regression method, the adaptive feature fusion data of the multi-source remote sensing precipitation data is downscaled in combination with the influencing factors of precipitation, so as to obtain the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data; According to the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with the improved high-precision surface modeling method, a multi-source precipitation fusion model is constructed. 2. The method for adaptive fusion of multi-source remote sensing precipitation data according to claim 1 is characterized in that the adaptive feature fusion data of the multi-source remote sensing precipitation data is downscaled by using the geographically weighted ridge regression method in combination with the influencing factors of precipitation to obtain the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data, which is specifically: According to the following expression:

, Downscaling the adaptive feature fusion data of the multi-source remote sensing precipitation data; In the formula,

is the regression function constructed by the geographically weighted ridge regression method; v is the adaptive feature fusion data of the multi-source remote sensing precipitation data; covariate is the covariate set, that is, the set of factors affecting precipitation; x0 is the _downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data. 3. The adaptive fusion method for multi-source remote sensing precipitation data according to claim 2 is characterized in that the expression of the multi-source precipitation fusion model is as follows:

, Wherein: A, B, C are coefficients of the finite difference equations corresponding to the high-precision surface modeling method; d, q, p are the right-hand side terms of the finite difference equations corresponding to the high-precision surface modeling method; x ⁿ⁺¹ represents the value of the n+1th iteration of each grid point on the simulation surface corresponding to the high-precision surface modeling method; S is the sampling matrix; g is the sampling vector;

is the regression function constructed by the geographically weighted ridge regression method; v is the adaptive feature fusion data of the multi-source remote sensing precipitation data; covariate is a set of covariates, that is, a set of factors affecting precipitation ^; x0 is the downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data, which serves as the initial surface of the precipitation spatial distribution corresponding to the current iteration of the high-precision surface modeling method; H and L are respectively the upper and lower bounds of each grid point on the simulation surface corresponding to the high-precision surface modeling method, which is different from the traditional high-precision surface modeling method that only uses meteorological station constraints. 4. The method for adaptive fusion of multi-source remote sensing precipitation data according to claim 1, wherein the expression of adaptive feature fusion data of multi-source remote sensing precipitation data is as follows:

, Wherein: v represents the adaptive feature fusion data of the multi-source remote sensing precipitation data;

,

are the mean square errors of the precipitation data from the ith data source and the jth data source respectively; ui represents the precipitation data from the ith data source; _k represents the total number of data sources. 5. The method for adaptive fusion of multi-source remote sensing precipitation data according to claim 3 is characterized in that after constructing a multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data, combined with an improved high-precision surface modeling method, the method further comprises: The multi-source precipitation fusion model is solved by using the preconditioned conjugate gradient method and multiple iteration steps. Under the optimization control constraints of the meteorological station observation data and upper and lower bounds, the initial surface x ⁰ of precipitation spatial distribution is continuously adjusted to finally obtain the optimal estimation value of precipitation spatial distribution. 6. The method for adaptively fusing multi-source remote sensing precipitation data according to claim 5, further comprising: For each iteration, the following processing is performed on each grid point on the simulation surface: If there is no meteorological station at the current grid point, the upper and lower bounds H and L of the current grid point are determined according to the relaxation coefficient of the high-precision surface modeling method and the extreme value of the neighboring grid points within the search radius of the high-precision surface modeling method; Wherein, the search radius is the number of adjacent grid points that need to be searched when the high-precision surface modeling method determines the upper and lower bounds H and L of the current grid point; If the number of meteorological stations in the current grid point is less than the preset threshold, the value of the neighboring grid point within the search radius is defined as the average of the observation value of the existing meteorological station within the radius and the grid point value of the multi-source remote sensing precipitation data within the search radius, and x ⁿ⁺¹ satisfies the inequality

. 7. The method for adaptively fusing multi-source remote sensing precipitation data according to claim 5, characterized in that: For each iteration, the sampling point weights corresponding to each meteorological station are determined by the following steps: Calculate the average value of the neighboring grid points of each meteorological station on the current iteration simulation surface; The difference between the observed data of each meteorological station and the average value is calculated, and the calculated difference is used as the sampling point weight corresponding to each meteorological station. 8. A multi-source remote sensing precipitation data adaptive fusion system, characterized by comprising: A weight calculation unit is configured to calculate the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data by using the Lagrange multiplier method based on the error characteristics of the multi-source remote sensing precipitation data; The expression of the error characteristic of the multi-source remote sensing precipitation data is as follows:

, Where: σ ² is the mean square error; E represents the expected value; u represents the real precipitation data, u _i represents the precipitation data of the i - th data source; ω _i represents the weight corresponding to the precipitation data of the i- th data source; v represents the adaptive feature fusion data of the multi-source remote sensing precipitation data; k represents the total number of data sources; The weight calculation unit is further configured as: The Lagrange multiplier method is used to solve the expression of the error characteristics of the multi-source remote sensing precipitation data to obtain the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data. The expression of the weight is as follows:

,

, Where:

,

are the mean square error of the precipitation data from the ith data source and the jth data source respectively; ω _i represents the weight corresponding to the precipitation data from the ith data source; k represents the total number of data sources; An adaptive feature fusion unit is configured to calculate adaptive feature fusion data of the multi-source remote sensing precipitation data based on the multi-source remote sensing precipitation data and the weight corresponding to the precipitation data of each data source in the multi-source remote sensing precipitation data; The data optimization unit is configured to use a geographically weighted ridge regression method to downscale the adaptive feature fusion data of the multi-source remote sensing precipitation data in combination with the influencing factors of precipitation, so as to obtain a downscaling result of the adaptive feature fusion data of the multi-source remote sensing precipitation data; The model building unit is configured to build a multi-source precipitation fusion model based on the downscaling results of the adaptive feature fusion data of the multi-source remote sensing precipitation data and the pre-acquired meteorological station observation data in combination with an improved high-precision surface modeling method.

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